The present invention relates to a method and apparatus for controlling coefficients of an adaptive filter for identifying an unknown system or predicting periodic signals using such adaptive filter, wherein interference signals are superimposed with the output signal from the unknown system. Practical applications of this method and apparatus include noise cancellers to eliminate noise mixed with a signal from a main input terminal, echo cancellers to eliminate undesired reflection signals acoustically coupled to a microphone from a speaker or mismatching of 2-line to 4-line conversion circuit, line equalizers to equalize distortion caused by transmission lines and adaptive line enhancers to pick up periodic signals buried in a wideband signal or to suppress periodic interference signals in a wideband signal.
In identifying unknown systems or predicting periodic signals using an adaptive filter, noise cancellers and adaptive line enhancers (referred to as ALE hereunder) are known as typical examples where strong interference signals are superimposed with an output signal from an unknown system. See p.p. 1692-1716 of the PROCEEDINGS OF IEEE, 1975; Vol. 63, No. 12 (referred to as the Reference 1 hereunder). Also known are echo cancellers as disclosed in the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, 1984, Vol. 2, No. 2 at p.p. 283-297 (referred to as the Reference 2 hereunder). In echo cancellers, if double talk is not detected properly, the near-end signal acts as a strong interference signal. No double talk detection is made in echo cancellers to be used in 2-line bidirectional transmission. In this case, additional noise superimposed in the transmission lines will be a weak interference signal to the adaptive operation of the filter.
A noise canceller suppresses noise in the signal by applying a noise replica corresponding to the noise components in the main input terminal. Used for this end is an adaptive filter having a transfer function similar to the impulse response of the noise path from the noise source to the main input terminal. At this time, a coefficient for each tap of the adaptive filter is successively modified by correlating the reference noise derived at the reference input terminal with a difference signal obtained by subtracting the noise replica from the mixed signal of the noise and the signal.
On the other hand, an echo canceller suppresses the echo by subtracting a pseudo echo or an echo replica from the echo signal caused by mismatching of the 2-line to 4-line conversion circuit in a 2-line bidirectional transmission line or a long distance telephone line or acoustical coupling between a microphone and a speaker. The echo replica is generated by using an active filter having a transfer function similar to the impulse response of the echo path. A coefficient of each tap at the adaptive filter is successively modified by correlating the reference signal at the reference input terminal with a difference signal obtained by subtracting the echo replica from the mixed signal of the echo signal and the additional noise.
Used in ALEs is an adaptive filter having a transfer function to pass only signal components whose periods are equal to those of the periodic signals for enhancing the periodic signals buried in a wideband signal. A coefficient of each tap of the adaptive filter for this application is a prediction coefficient to predict the periodic signals. It is successively modified by correlating the difference signal obtained by subtracting the predicted periodic signals or the output from the adaptive filter from the mixed signal of the periodic signals and the wideband signal on the main input terminal with the delayed mixed signal on the reference input. For enhancing the periodic signals, the output from the adaptive filter is used as the ALE output and the ALE is also used to suppress periodic interference signal to the wideband signal. In the latter case, the output signal is the difference or error signal instead of the output from the adaptive filter.
There are two typical coefficient modifications or converging algorithms. One is an LMS algorithm (see the Reference 1). The other is a Learning Identification Method (LIM) as set forth in p.p. 282-287 of The IEEE Transactions on Automatic Control, Vol. 12, No. 3 in 1967 (referred to as Reference 3 hereunder).
Illustrated In FIG. 14 is a block diagram of a conventional noise canceller. A mixed signal of a signal and noise detected on a main input terminal 1 is supplied to a subtracter 4. On the other hand, supplied to an adaptive filter 3 is a reference noise detected on a reference input terminal 2. The noise components are cancelled by the subtracter 4 which subtracts the noise replica generated by the adaptive filter 3 from the mixed signal. The subtracted output is supplied to an output terminal 6. Simultaneously, the output of the subtracter 4 is supplied to a multiplier 5 to be multiplied by the coefficient 2.alpha. to be used for correcting the coefficient of the adaptive filter 3. Here, .alpha. is a constant and 2.alpha. is known as a step size. Let the signal, the reference noise, the noise to be cancelled and an additional noise to the signal be S.sub.k (k being an index to represent time), n.sub.k, V.sub.k and .delta..sub.k, respectively. The signal u.sub.k to be actually supplied to the subtracter 4 from the input terminal 1 is given by the following expression: EQU u.sub.k =S.sub.k +V.sub.k +.delta..sub.k ( 1)
A purpose of the noise cancellers is to generate the noise replica V.sub.k of the noise components v.sub.k in the above expression (1) for cancelling the noise. The noise replica V.sub.k is adaptively generated by using a closed loop comprising the adaptive filter 3, the subtracter 4 and the multiplier 5 in FIG. 14. The closed loop provides the difference or error signal d.sub.k given by the following expression as the output signal from the subtracter 4. However, it is to be noted that .delta..sub.k is sufficiently small as compared to S.sub.k and is neglected in the expression: EQU d.sub.k =S.sub.k +v.sub.k -V.sub.k ( 2)
In the above expression (2), (v.sub.k -V.sub.k) is known as a residual noise. In the LMS algorithm, the m-th coefficient C.sub.m,k of the adaptive filter 3 is corrected in accordance with the following expression: EQU C.sub.m,k +C.sub.m,k-1 +2.alpha..multidot.d.sub.k .multidot.n.sub.m,k-1( 3)
A matrix format of the expression (3) for all of the N coefficients is as follows: EQU C.sub.k =C.sub.k-1 +2.alpha..multidot.d.sub.k .multidot.n.sub.k-1( 4)
Where, C.sub.k and n.sub.k are given by the following expressions, respectively: EQU C.sub.k =[C.sub.0 C.sub.1 . . . C.sub.N-1 ].sup.T ( 5) EQU n.sub.k =[n.sub.k n.sub.k-1 . . . n.sub.K-N+1 ].sup.T ( 6)
Here, [.].sup.T represents a transposition of the matrix. On the other hand, in the LIM algorithm, correction of coefficients will be carried out in accordance with the following expression (7) rather than the expression (4). EQU C.sub.k =C.sub.k-1 +(2.mu./N.sigma.n.sup.2).multidot.d.sub.k .multidot.n.sub.k-1 ( 7)
.mu. in the above expression (7) is the step size for LIM and .sigma..sub.n.sup.2 represents an average power of the input to the adaptive filter 3. .sigma..sub.n.sup.2 is used to make the step size .mu. counter proportional to the average power for stable convergence. There are a few methods to calculate .sigma..sub.n.sup.2. One example is to calculate in accordance with the following expression (8): ##EQU1##
The step sizes in the above expressions (4) and (7) define the converging speed of the adaptive filter and the residual noise level after convergence. In case of the LMS algorithm, if the value of .alpha. is larger, the convergence speed is faster but the final residual noise level increases. On the contrary, it is required to choose relatively small value of .alpha. in order to achieve a sufficiently low final residual noise level. However, this causes a relatively slow convergence speed. This is true of the step size .mu. in the LIM algorithm.
A VS algorithm has been proposed in order to meet the conflicting requirements in the step size to the converging speed and the final residual noise. See p.p. 309-316 of the IEEE Transactions on Acoustics, Speech and Signal Processing, 1986, Vol. 34, No. 2 (referred to as Reference 4 hereunder). The VS algorithm uses step size matrix 2A instead of the step size 2.alpha. in the LMS algorithm as represented by the above expression (4). Each component of A is controlled in response to the progress in convergence of the adaptive filter. The use of individual step size given by the step size matrix A rather than a common step size for each coefficient allows optimum step size for each coefficient depending on variations in magnitude of the self-correlation matrix component, thereby improving the converging speed. Actual correction of the coefficients will be performed by the following expression: ##EQU2## a.sub.m,m is determined by the successive pattern of the polarity sgn [G.sub.m,k ] of the gradient component G.sub.m,k corresponding to the m-th tap, where G.sub.m,k is given by the following expression: EQU G.sub.m,k =2.multidot..alpha..sub.m,m .multidot.d.sub.k .multidot.n.sub.m,k-1 ( 10)
In an ideal case where d.sub.k =v.sub.k -V.sub.k, the polarity of G.sub.m,k directly represents the progress of convergence. However, d.sub.k is generally affected by S.sub.k as understood from the expression d.sub.k =S.sub.k +v.sub.k -V.sub.k. In order to reduce the influence of S.sub.k, a.sub.m,m is halved if sgn [G.sub.m,k ] changes m.sub.o times consecutively. On the other hand, it is doubled if sgn [G.sub.m,k ] are equal for m.sub.1 times consecutively. That is, the VS algorithm features to make equivalently S.sub.k +v.sub.k -V.sub.k .varies.v.sub.k -V.sub.k by detecting succession of identical polarities or successive alternations of the polarity. However, there is a certain limitation In the variable range of a.sub.m,m. That is, the maximum value .alpha..sub.max =1/.lambda. and the minimum value .alpha..sub.min is defined by a desired final residual noise. Here, .lambda. is the maximum inherent value of the autocorrelation matrix. The performance of the VS algorithm depends largely on the relationship between S.sub.k and v.sub.k -V.sub.k. The polarity changing pattern of the above G.sub.m,k is a function of the signal-to-noise ratio (SNR) and the spectrum of S.sub.k. When the SNR is large, .vertline.S.sub.k .vertline.&gt;.vertline.v.sub.k -V.sub.k .vertline. is almost always true and seriously affects polarity detection. Considering the fact that SNR is defined by the ratio of the signal and the noise in mathematical expectation of their instantaneous powers, .vertline.S.sub.k .vertline.&gt;.vertline.v.sub.k -V.sub.k .vertline. is satisfied with a greater probability as S.sub.k contains more higher-frequency components even if SNR is low. In other words, when S.sub.k has many peaks and dips, it is most likely that .vertline.S.sub.k .vertline. is larger than .vertline.v.sub.k -V.sub.k .vertline. in some of the peaks even if SNR is sufficiently low.
Illustrated in FIG. 15 is a block diagram of a conventional ALE corresponding to the noise canceller in FIG. 14. A mixed signal to be supplied to an input terminal 1 comprises a wideband signal S.sub.k, a periodic signal v.sub.k and an additive noise .delta..sub.k. On the other hand, supplied to an adaptive filter 3 is a delayed signal of the mixed signal on the input terminal 1 delayed by L by a delay element 8 and is given by: EQU u.sub.k-L =S.sub.k-L +V.sub.K-L ( 11)
However, .delta..sub.k is neglected in the above expression (11) because it is sufficiently small compared with S.sub.k. The difference signal d.sub.k given by the expression (2) is obtained by subtracting the prediction signal V.sub.k of v.sub.k generated by the adaptive filter 3 from the mixed signal u.sub.k of the expression (1). Derived from an output terminal 6 is a wideband signal with suppressed periodic interference signals. Also derived from an output terminal 7 is the enhanced periodic signals obtained by suppressing wideband noise. Coefficient correction of the adaptive filter 3 should be carried out by using (v.sub.k -V.sub.k) which is a prediction error of the periodic signals. However, the actually derived difference signal d.sub.k contains the wideband signal S.sub.k. As a result, the above discussions on .vertline.S.sub.k .vertline. and .vertline.v.sub.k -V.sub.k .vertline. in the noise canceller are also applicable to the ALE. That is, a correct step size control in the VS algorithm depends on the relationship between .vertline.S.sub.k .vertline. and .vertline.v.sub.k -V.sub.k .vertline. and no correct step size is obtained if .vertline.S.sub.k .vertline. is larger than .vertline.v.sub.k -V.sub.k .vertline..
Illustrated in FIG. 16 is a block diagram of a conventional echo canceller corresponding to the noise canceller in FIG. 14. The block diagrams in FIGS. 16 and 14 are identical to each other but differ only in input signals. Supplied to an input terminal 1 is a signal comprising an echo V.sub.k and an additive noise .delta..sub.k. EQU u.sub.k =v.sub.k +.delta..sub.k ( 12)
On the other hand, supplied to an adaptive filter 3 is n.sub.k through an input terminal 2. n.sub.k represents an input signal to a 2-line to 4-line conversion transformer in case of a bidirectional transmission circuit or a signal to be supplied to a speaker in case of an echo due to acoustic coupling. An echo replica V.sub.k of v.sub.k generated by the adaptive filter 3 is subtracted from u.sub.k in the expression (12) derived from the input terminal 1 to obtain the difference signal d.sub.k in the following expression (13): EQU d.sub.k =v.sub.k -V.sub.k +.delta..sub.k ( 13)
Derived from an output terminal 6 is the echo cancelled signal. Coefficient correction of the adaptive filter 3 should be performed using the residual echo (v.sub.k -V.sub.k). In practice, however, the additional noise .delta..sub.k is contained in the difference signal d.sub.k. Although .delta..sub.k is fairly small in general, it interferes the residual echo when the residual echo becomes sufficiently small.